Transition from the vortex state to the Fulde–Ferrell–Larkin–Ovchinnikov state in quasi-two-dimensional superconductors

Abstract

We examine the coexistence of the vortex state and the Fulde–Ferrell–Larkin–Ovchinnikov (FFLO) state in quasi-two-dimensional type-II superconductors and the transition from this mixed state to the pure FFLO state when the Maki parameter α increases. The pure FFLO state, which is characterized by Cooper pairs having finite center-of-mass momenta q≠0, occurs in the two-dimensional limit when the magnetic field is parallel to the conducting plane. The vectors q are determined from the Fermi-surface structure and pairing anisotropy, and become finite below a temperature T∗. In quasi-two-dimensions, because of the orbital pair-breaking effect, a mixed state characterized by (n,q∥) occurs, where n and q∥ denote the Landau-level index of the vortex state and the wave number of the additional FFLO modulation along the magnetic field. We obtain the α dependence of the upper critical field by numerical calculations. The upper critical field exhibits a cascade curve in the H−T phase diagram. It is analytically shown that n diverges in the two-dimensional limit α→∞ below T∗. In this limit, the upper critical-field equation for the mixed state reduces to that for the FFLO state. A relation between n of the mixed state and q⊥ of the pure FFLO state is obtained, where q⊥ denotes the component of q perpendicular to the magnetic field. It is found that the pure FFLO state is nothing but the vortex state with infinitely large n as is known in two-dimensional superconductors in a tilted magnetic field. The vortex state with large n can be regarded as the FFLO state with nonzero q⊥ in three dimensions.

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